Questions tagged [factorization]
Questions on factoring various types of mathematical expressions, with the use of Factor, FactorInteger, FactorSquareFree and related commands.
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Polynomial factorization over number fields that are extensions of the rationals [duplicate]
I want to factor some polynomials into irreducible terms, but not only limited to integers.
If I evaluate Factor[x^4+1], it will generate nothing.
But in fact I ...
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Factor out constant terms with square roots
I would like to use FactorTerms to factor out constant numerical terms out of an expression, this works as follows:
...
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Prime factorization of numerator and denominator of rationals
I am completely new to Mathematica and I need some help (sorry if it is trivial, but I haven't found the answer). I have this code
...
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How to factor exponents?
Given
Exp[a+b]
I want to turn it into
Exp[a] Exp[b]
How can I achieve this in general? That is I am looking for more or ...
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Checking whether one polynomial is a factor of another
Given two polynomials, $f(x)$ and $g(x)$, I need to determine whether $f(x)$ is a factor of $g(x)$. Seems simple enough, and the way I initially did it was just checking if $f(x)$ is in a FactorList ...
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Advanced Trivariate Polynomial With Integer Coefficients Manipulation
Suppose $$f(a,b,c)=\left(a+b+c \right)^{2}-2 \left(a^{2}+b^{2}+c^{2}\right)-4abc$$ and $g(a,b,c)$ is some polynomial of total degree 6 with integer coeffients.
I want to find a polynomial $h(x)$ with ...
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How can Mathematica take a prefactor in front of the relation
I have the following term in an expression
$$\frac{q_B' \sin2q_B}{P_B Q_B^2}(2 Q_B P_B - \sin^2 q_B \Pi_B) q_1 q_1'$$
the prime denotes differentiation w.r.t a coordinate. Some additional ...
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wrong LUDecomposition - first row is the last one
I am having a huge problem with my Mathematica notebook.
I am trying to evaluate LUDecomposition and it keeps getting wrong - when I multiply ...
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How to convert an expression a + b*Sqrt[c] to a simpler format?
Example: we have the following expansions:
...
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how to extract the elements of the output of FactorInteger function? [closed]
For example, when I evaluate
FactorInteger[265^2 - 87463]
the output is
{{-1, 1}, {2, 1}, {3, 1}, {13, 2}, {17, 1}}
I ...
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Factor by a specific literal (i.e factor by $s^N$ a transfer function)
I've found the closed loop transfer function but I want to know the order of it. So, the idea is to factor the denominator by the highest exponent of s to get an expression like this one:
$$
l(s)=g(s)...
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factorization of integer into two parts with specific prime factors
I would like to write a Mathematica code to decompose an integer into two or more parts with primes in special intervals.
For instance, I want to decompose $m=\binom{n}{k}$ into two parts U and V ...
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Scalar multiplication of an expression containing equality [duplicate]
Suppose:
expr=(a x + a y==0);
expr/a
(*Out:=(a x + a y==0)/a*)
I want a eliminated to obtain ...
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Factor Recursively
I'm looking for a way to factor a polynomial recursively. Consider the following example:
expr = Expand[(a + (b + c)^2)^2];
Factor@expr
Simplify@expr
While the ...
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Factorisation diagrams
Here is a way to visualize the factorisation of natural numbers. How do we get this or a similar kind of output using Mathematica?
See the list of images generated for number from 1 to 36:
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Why Mathematica can not factorize polynomials over algebraic fields?
I noticed that a factorization over algebraic fields is useless in Mathematica. Here is the example over the field containing I*Sqrt[3]:
...
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How to factorize polynomials into "shortest possible" pieces
I am using Factor a lot in my work, it is extremely versatile and efficient, except for one aspect. Example: ...
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Why is Mathematica factoring I out of real expressions, and how can I reverse it?
I am doing some complicated series expansions involving integrals and whatnot, but everything is real the whole time (and I specify that using Assumptions at every ...
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Factorize expression into matrix/vector operations if possible
I'd like to let MMA factorize an expression (tensor) into matrix operations if that's possible.
Example – there's an expression P1 and I want MMA to create another ...
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Put in evidence and return 1 if already fully factorised
Does anyone have a clever idea how to get the overall factor in front of a polynomial or just return 1 if everything is already put in evidence ?
Here is an example with a dummy ...
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Simplify with Integer Factorization
I have some outputs of Solve applied to algebraic equations with combinatorial coefficients (i.e. integers), and I'd like to see the results from ...
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Collect function with iterator issue
I've got the following code for the first few terms of an expansion. I want to collect the terms in increasing powers of (s/r) but using an iterator. The code is as ...
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Factor Denominator of Fraction [closed]
How do I get Mathematica to factor the denominator of a fraction? For example, to turn
$$\frac{1}{s^2+3s+2}$$
into
$$\frac{1}{(s+1)(s+2)}.$$
I tried Factor, but it ...
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Powers of prime factors of a positive integer $n$ in "Mathematica"?
I would like to find the powers of a prime in the unique prime factorization of an $n$. I want a function $f[n,p]$ such that $n,p$ are given and I need to know what the power of $p$ is. For instance
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What prevents Factor from Working also on Arguments of Sqrt in Expressions?
Consider this example (intersection of a line and a sphere):
...
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Factorization of a polynomial fraction to a certain combinations of other polynomial fractions
I currently am working on a project for to find some new algebra structures. But I faced with a factorization problem which I cannot come out of it! I could find the lower dimensional of it. But I ...
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Factor a polynomial over the reals
I can't seem to find a function in Mathematica that factors a polynomial over the reals. Obviously, Factor doesn't work since it works over the integers, over $\mathbb{Z}_p$, or some algebraic fields ...
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Efficiently create a list of factors of consecutive integers
I'm interested in a scalable (read: sublinear) algorithm for producing the list of integer factors of each integer from 1 to n. ...
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Factoring for exponents
How can I factorise into powers of integer exponents?
An expression such as,
...
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Trouble factoring an expression
I've got the term $-1 + 2b^2 + 2b\sqrt {b^2-1}$ appearing several times within several larger expressions. It is easy to see that this expression factors into ${(b+\sqrt{b^2-1})^2}$, but when I use <...
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Rewrite a real polynomial in real (but only linear and quadratic) factors
According to my calculus book: "Every real polynomial can be factored into a product of real (possibly repeated) linear factors and real (also possibly repeated) quadratic factors having no real zeros....
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How can I factor my trigonometric equation?
The equation
$$3\sin^2 x - 3\cos x -6\sin x + 2\sin 2x + 3=0$$
has a solution $x = 0$. That means it has a factor of $\cos x - 1$. I tried to write the given equation has the form
$$(\cos x - 1)P(...
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Selecting terms on only one variable from a multiple-variable expression
Say I have a polynomial like
$x y^2+15x^2 y+x+3y+10$
and I want to obtain, say, only the coefficient in $x$ alone, namely a 1. Using
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How to efficiently find only the rational roots of a rational complex polynomial?
I need to find all the rational roots of a bunch of high-order polynomials with rational complex coefficients. Is there an efficient way to do this?
My best effort on an example polynomial:
...
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Collect/Factor a fraction
Is there a way to tell Mathematica to factor things only containing a specific combination of a fraction, example:
$$\tag{1}f = \frac{a+m\cdot a+b+n\cdot b+c+k\cdot c+d+e}{ab}$$
Is there a way to ...
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Can Mathematica factor a polynomial over an algebraic number field?
If I input:
Factor[x^2 + x + 1, Extension -> Sqrt[-3]]
Mathematica returns:
...
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Formatting the prime factorization of expressions
I have a series expansion in $x$ and $a,b$ are constants which I want to type in $\LaTeX$. But the numbers/integers are pretty large (have a lot of digits) so it becomes a bit messy in $\LaTeX$. ...
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Timing and ListPlot
I am currently trying to examine the Timing function as it relates to generating primes and factorize large integers. What I want to do is to visualize how time ...
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Finding a seven-digit number with all of its prime factors less than 20? [closed]
How can I find a seven-digit number with all of its prime factors less than 20?
I have no clue how to do this.
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One of the factors greater than $x$
Is there an easy way to tell Mathematica to find one of the prime factors of $n$ greater than $x$. For example, if $n=1299709\cdot 7919 \cdot 17$, is there a way to request a factor greater than $100$....
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Represent a positive integer as a product of its factors
I am trying to illustrate some simple ideas with exponents. I can manually express something like $5^4$ as $5 \cdot 5 \cdot 5 \cdot 5$, but wondered how to get Mathematica to do that for me.
I ...
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Selecting divisors of a large number that meet some criteria using the factors list
I have a list that represents a factorization of a number: its format is identical to the output of FactorInteger. I need to select the divisors that meet some ...
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Factor fraction, where variable occurring in both, numerator and denominator, only appears once
I have an expression like $$\frac{1+a^2+2 a \cos\left(p\right)}{\left(1+b^2\right)z-1-a^2-2 \left(a+b z\right)\cos\left(p\right)}\text{.}\tag{1}$$
Is there a combination of Mathematica functions to ...
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Factoring rationals from equation based on digit complexity?
Consider an equation of the following type:
( poly = (3 x)/35 + (6 y)/7 ) == 0
If we apply the command Factor to this ...
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How to replace $-x^{}\,y^*-y^{}\,x^*$ by $-(x^{}\,y^*+y^{}\,x^*)$?
Up to now, I have tried some codes like the following:
...
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decomposing an expression into absolutely positive terms
I have a big ugly expression which, for unimportant (here) reasons, must be greater than or equal to zero. It is formed from terms which themselves are greater than or equal to zero.
As such it ...
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Factoring out a common term
Very simple question, but I can't find a simple answer here or in the documentation. I have an expression:
qq = a x + b x^2 + c x^3
and wish to factor out a ...
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